Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models

• URL: http://arxiv.org/abs/2304.13205v1
• Date: Wed, 26 Apr 2023 00:11:00 GMT
• Title: Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models
• Authors: Simin Shekarpaz, Fanhai Zeng, and George Karniadakis
• Abstract summary: We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs) The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems and demonstrates improved accuracy through its application to neuron models. Specifically, we apply operator splitting to decompose the original neuron model into sub-problems that are then solved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractional derivatives in fractional neuron models, leading to improved accuracy and efficiency. The results of this study highlight the potential of splitting PINNs in solving both integer- and fractional-order neuron models, as well as other similar systems in computational science and engineering.

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